Title	Knot-theoretic ternary quasigroup theory and shadow biquandle theory for oriented surface-knots
Creator	Oshiro (Shoda), Kanako
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-11-07T11:16
Description	A knot-theoretic ternary quasigroup is an algebraic system which equips a ternary operation coming from oriented (surface-)knot diagrams with region labelings. A shadow biquandle is an algebraic system which equips two binary operations and an action coming from oriented (surface-)knot diagrams with semi-arc (or semi-sheet) labelings and region labelings. Note that the region labeling by a shadow biquandle depends on the semi-arc (or semi-sheet) labeling whereas the region labeling by a knot-theoretic ternary quasigroup does not. In this talk, we show that under some condition, knot-theoretic ternary quasigroup theory and shadow biquandle theory are the same: Homology groups are the same; cocycle invariants for oriented surface-knots are the same.
Extent	41.0 minutes
Subject	Mathematics; Manifolds And Cell Complexes
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Sophia University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2020-05-06
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0390366
URI	http://hdl.handle.net/2429/74346
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

Open Collections

BIRS Workshop Lecture Videos

Knot-theoretic ternary quasigroup theory and shadow biquandle theory for oriented surface-knots Oshiro (Shoda), Kanako

Description

Item Metadata

Item Media

Item Citations and Data

Rights